A very unsentimental education it was, too. Nick Hornby has adroitly adapted and given a dramatic shape to the bestselling memoir by Lynn Barber, telling the true story of how, in the early 1960s, she was seduced as a 16-year-old schoolgirl by an older man. This sociopathic charmer's seduction crucially extended to her poor old mum and dad, dazzling them into being complicit in the arrangement; along with their daughter, they went into a clenched denial about what was happening.

Seen from a certain angle, that could look like misery-lit, a story of sex abuse and class shame, were it not for the fact that it is extremely funny. Hornby's screenplay catches the stranger-than-fiction absurdity nicely, and, although he softens the most excruciating moment from Barber's book, his script gives the audience a clear view of the painful delusions of all concerned. Lone Scherfig directs, and there is a wonderful performance from 24-year-old newcomer Carey Mulligan as Lynn – here renamed Jenny – the heartbreakingly vulnerable pseudo-sophisticate earnestly cramming for her Oxbridge exams, and longing for real experience.

Cara Seymour and Alfred Molina play Jenny's parents, the mother a kindly soul, sensitive to her daughter's unformed yearnings, the dad a grumpy martinet: a great insister on homework and obsesser on the subject of all the money he's forking out on school fees, uniform, etc.

One rainy day, when Jenny is carrying her cello home from an orchestra rehearsal, super-smooth David pulls up in his flashy car and coolly offers her a lift. He is played by American actor Peter Sarsgaard with a slowish, carefully enunciated English voice that by accident or design really does sound very creepy. David captivates her with his casual directness, his exotic Jewishness, his worldly manner. David has a compulsive liar's sixth sense for other people's weaknesses. He picks up on Jenny's need to be taken seriously – and to escape.

On being invited back to meet her parents, David walks into their modest living room to catch Jenny's father Jack making an apparently antisemitic remark. He had been blathering about one of Jenny's old boyfriends being a "wandering Jew", simply because of his gadabout ways. It's an innocent turn of phrase, but with an instinctive strategic brilliance worthy of Stephen Potter's Lifemanship academy, David puts Jack at a disadvantage. Dad will now have to allow him to take his daughter out – or else be thought a bigot. Soon David is turning the charm on her parents, turning them into his simpering, giggling fans, and he introduces Jenny to a thrilling new world of restaurants, nightclubs and naughty weekends in Paris. Shamingly, her dad abandons his strictness and turns a blind eye to everything, hoping this apparently rich man might marry her. But there is a dark side to David: he is a chancer, a fantasist and a seedy underling of slum landlord Peter Rachman. He is also deeply strange in bed, with his baby-talk and weird, fastidious lack of enthusiasm for the act itself. Jenny is on the brink of throwing her future away on a tacky illusion.

Some of the best parts of the film show Jenny's dreamy delight in going out à quatre with David and his glamorous friends Danny and Helen, played by Dominic Cooper and Rosamund Pike. At last, she is being treated like a grownup! Pike is outstanding as the faintly vacant and glassy-eyed Helen who is nonetheless entirely aware of what Jenny is feeling, and becomes the nearest thing she has to a real friend. When they first meet, Jenny reaches across and wonderingly strokes Helen's fur coat, like a child, before she can stop herself. "Yes, it's lovely isn't it?" smiles Helen – gentle, understanding, knowing not to make Jenny feel small.

The story, as it is played out, is not too far from the kitchen-sink dramas from the 60s era of Billy Liar and A Taste of Honey. Traditionally, it's the working-class girl who gets above herself, gets into trouble and has to get it sorted. But this girl is middle class and pregnancy isn't what happens: what is aborted, or almost aborted, is Jenny's Oxford career. Her horrible and quite genuinely antisemitic headmistress – a great cameo from Emma Thompson – expels her on learning that she is engaged to a Jew. In the book, there is a brilliantly awful and all-too-real moment when her poor old dad has to go cap-in-hand to the headmistress after the affair has collapsed, begging her to let his humiliated daughter return and sit the Oxbridge exams after all. In the film, Jenny stays heroically defiant, and gets private coaching.

So why on earth didn't Jenny question her shabby lover more closely? In the book, Barber semi-seriously claims it was because her teenage self affected a ropey suburban existentialism that forbade such questioning as "bourgeois". Hornby's script suggests that this wasn't exactly it. She was simply conned, hobbled by her English politeness, and ashamed of her English lack of sophistication. She was taken in, as we all could be, by someone brazen enough to believe in his own lies. It's a sad, painful comedy, and the lovely performance from Mulligan makes it a very enjoyable film.